8. 8
Fundamentals of Electron Optics
Refraction and reflection of Electron beam when encountering the
region of potential difference.
( ) 1
( ) 2
Sin r V
Sin i V
An electron passing from a lower potential V1 to higher potential
V2 undergoes refraction as defined by Snell’s law.
i
r
V1 V1
V2 V2
i
V1 V1
V2 V2
V1<V2
V1>V2
r’
r
9. 9
( ) 1
( ) 2
Sin r V
Sin i V
1
2
V
i Sin
V
1
2
V
i Sin
V
Refraction,
Reflection, r’ = i
Fundamentals of Electron Optics
Electron beam on passing through a region of potential difference
with V1<V2, experience a retardation making an angle of refraction
greater than incident angle.
13. Resolution: Power of resolving or identifying two closely spaced
particles separately
Limit of Resolution Where, NA numerical aperture of the
microscope
sin
NA n
nrefractive index of the media
Resolving Power of a Microscope
R∞
1
D R high , D low good microscope
D
0.61
D
NA
Optical microscope of λ=400 -700 nm, D>200
13
16. Depth of Field/Focus:
Another important aspect to resolution is the axial (or longitudinal) resolving
power of an objective, which is measured parallel to the optical axis and is most
often referred to as depth of field/focus.
When considering resolution in optical microscopy, a majority of the emphasis is placed
on point-to-point lateral resolution in the plane perpendicular to the optical axis.
It decreases with increased magnification. Sharpness of an
image depends upon the numerical aperture ‘NA’ and the
refractive index n of the lens material.
16
21. A Scanning Electron Microscope (SEM) is an instrument for observing
and analyzing the surface microstructure of a bulk sample using a finely
focused beam of electrons.
SEM can achieve 1 – 4 nm imaging resolution depending on the
instruments.
Primary Applications:
•Surface topography / morphology
•Composition analysis
•Contrast
•And more ……
What is Scanning Electron Microscope ?
21
23. Rotor
Rotary Pump
Air is drawn into the pump through an inlet
and it is compressed.
Consists of a stationary part, Stator and a
moving part, Rotor, assembled inside a
casing.
This rotor is driven by an electric motor at
a constant speed.
Vacuum System :
23
24. Diffusion Pump
Vacuum System :
It consists of a chamber housing a oil vessel with a
heater, a chimney and a nozzle. On chamber's outer
surface, cooling coils carrying water are wound.
The heater vaporizes the oil and these hot vapors
rise into the vapor chimney.
The hot vapors are deflected downwards by an
annular nozzle or a jet assembly mounted at the top
of the chimney.
This jet, moving downwards at supersonic speeds, imparts momentum to
randomly moving gas molecules in the chamber.
This momentum deflects the molecules towards the pump outlet.
A backing pump is constantly used to remove the gas molecules.
The hot oil condenses on cold walls and returns to the vessel at bottom. 24
25. Turbo Molecular Pump
Vacuum System :
It consists of alternate layers of stator and rotor discs.
The rotor rotates at a very high RPM.
The blades are mounted at an optimum angle, on
both stator and rotor.
This high speed rotation imparts momentum to the
gas particles upon collision with the rotor discs.
The high speed molecules are directed towards
the exit using the stator discs.
25
28. •“Gun Valve” separating the upper column from the rest of
the micro sample exchange; appropriate vacuum
•Use gloves when mounting samples and transferring
them to the column
•Samples are dry and free of excessive outgassing.
Precaution:
28
29. • There are three main types of gun –
Thermionic Gun - electrons are emitted from a filament when heated
sufficiently by passing current through it.
Field Emission Gun (FEG) - a very strong electric field is used to
extract electron from a material filament.
Thermal Field (Schottky) Emission Gun – electrons are ejected for
combined action of both heating and electric field.
Electron Source/Gun
29
Purpose:
Produce electrons
Roughly shape the beam
Set the electron energy (accelerating voltag
30. Thermionic Gun
•Filament is heated and begins to produce electrons.
•Electrons leave the filament tip with a negative potential so accelerate
towards the earthed anode and into the microscope column.
•A small negative bias on the Wehnelt then focuses the beam to a
crossover which acts as the electron source.
Example: Tungsten (W), Lanthanum hexaboride (LaB6)
30
31. Tungsten filament
assembly
Tungsten filament
LaB6 filament tip
• Can also use LaB6 crystal grown to a tip – gives a brighter
beam than W for same kV.
Thermionic Sources
Tungsten: Low work function
High Melting temperature ~ 3700 K
Emit electron at 2700K
31
32. •An extraction voltage of around 2kV is applied
to the first anode to create an intense electric
field to allow electrons to escape from the tip.
•The second anode is then used to accelerate
the electrons into the microscope at the
required energy.
•Combination of the two anodes focuses the beam into
a crossover creating a fine beam source.
• A very strong electric field (~109Vm-1) draws
electrons from a very fine metallic tip (usually
W).
FEG source – ZrO/W tip
Field Emission Gun (FEG)
32
33. Field Emission Gun (FEG)
Major Advantages:
•High resolution
•Very long potential source lifetime
• Low operating temperature (~300K)
• High brightness
• High current density (~1010 A/m2)
• Small source size < 0.01 um
• Highly spatially coherent, small energy
spread
Major Disadvantages:
•Small source size
•Not good for large area specimen, easy lose
current density
•Lowest maximum probe current.
•Poor current stability.
•Require ultra high vacuum in gun area.
In field emission, electrons tunnel through a
potential barrier, rather than escaping over it
as in thermionic emission.
33
36. 36
Thermionic Sources
Major Advantages:
•High resolution
•Very long potential source lifetime
• Low operating temperature (~300K)
• High brightness
• High current density (~1010 A/m2)
• Small source size < 0.01 um
• Highly spatially coherent, small energy
spread
Major Disadvantages:
•Small source size
•Not good for large area specimen, easy lose
current density
•Lowest maximum probe current.
•Poor current stability.
•Require ultra high vacuum in gun area.
Field Emission Gun (FEG)
Thermal Field (Schottky)
Emission Gun
37. 37
EM field exerts a force on a moving electron in a direction normal to both the field
and the propagation direction of the electrons.
41. Ideal and Actual lenses: Rays ideally focused to same plane. But, in reality
single focal plane does not occur.
41
42. Since the focal length ‘f’ of a lens is dependent on the strength of the
lens, it follows that different wavelengths will be focused to different
positions. Chromatic aberration of a lens is seen as fringes around the
image due to a “zone” of focus.
Lens Defects (Chromatic Aberration)
E +ΔE
42
43. The simplest way to correct for chromatic aberration is to use
illumination of a single wavelength!
Correction of Chromatic Aberration
In light optics chromatic aberration can be corrected by combining a
converging lens with a diverging lens. This is known as a “doublet” lens
Increase accelerating voltage which will
decrease spreading of electron energy
and make almost monochromatic
High accelerating voltage
43
44. Lens Defects (Spherical Aberration)
The fact that wavelengths enter and
leave the lens field at different angles
results in a defect known as spherical
aberration.
Peripheral Beam
Paraxial Beam
Aperture
Solution: Add a limiting aperture
44
48. Apertures
Advantages
Increase contrast by blocking
scattered Electrons
Decrease effects of chromatic
and spherical aberration by
cutting off edges of a lens
Disadvantages
Decrease resolution due to
effects of diffraction
Decrease resolution by
reducing half angle of
illumination
Decrease illumination by
blocking scattered electrons
48
57. Interaction Volume
The ‘interaction volume’ is the area of the sample excited by the electron
beam to produce a signal.
The penetration of the electron beam into
the sample is affected by the accelerating
voltage used, the higher the kV the greater
the penetration.
The effective interaction volume can be
calculated using the electron range, R:-
1.67
0
0.89
0.0276
( )
AE
R m
Z
Where
A atomic weight (g/mole),
Z atomic number,
ρ density (in g/cm3)
Eo energy of the primary electron beam (in kV).
Accelerating voltage
(kV)
Primary Electron
Range (µm)
50 3.1
30 0.99
5 0.16
1 0.01 (10 nm)
Fe A=55.85, Z=26, ρ=7.78 g/cm3
57
59. 1 kV 5 kV
15 kV
Accelerating Voltage
The dimensions of
the interaction
volume increases
with accelerating
voltage
The probability of
elastic scattering is
inversely proportional
to beam energy
59
60. Depth based information
Surface based information
Accelerating voltage reduction reduced interaction volume surface information 60
62. C, 6 Fe, 26
Au, 79
Atomic Number
The dimensions of the
interaction volume will
decrease with higher
atomic number
elements.
The rate of energy
loss of the electron
beam increases with
atomic number and
thus electrons do not
penetrate as deeply
into the sample
The probability of elastic
scattering increases with
A – causing the
interaction volume to
widen.
Accelerating voltage, 5kV
62
63. The angle at which the beam
strikes the specimen and the
distance from the surface are
important factors in how much of
signal escapes from the specimen.
63
64. Elements of different atomic number
SE or BSE emitted from different element are different , create
different contrast in image 64
70. ‘Light’ region is made up predominantly of Fe.
(i.e. the heaviest element)
‘Grey’ region is made up predominantly of Ca.
‘Dark’ region is made up predominantly of Si
and Al. (i.e. the lightest elements)
Energy Dispersive Spectroscopy on the SEM
• There were 3 distinct regions in the Backscattered Image
Back scattered electrons are deflected more by heavier atoms leading to a brighter
contrast in BEI images – the lighter the region the heavier the element present.
The Y-axis shows the counts (number of X-rays
received and processed by the detector) and the
X-axis shows the energy level of those counts.
70
71. An electron microscope is operating with an accelerating voltage
~100KV under vacuum of ~10-8 mbar. If half angle of incident beam
cone is 0.01 radian, what will be the resolution of the electron
microscope? [sin(0.01rad)=0.00999, h=6.62x10-34m2 kg / s, e=1.6x10-19C
, m=9.1x10-31kg]
For electron energy of 10kV, calculate the interaction volume of Fe
having A=55.85, Z=26, ρ=7.78 g/cm3
Where
A atomic weight (g/mole),
Z atomic number,
ρ density (in g/cm3)
Eo energy of the primary electron beam (in kV).
71
As the term says we are utilizing transmission mode of the electrons to find out the features inside the materials. So in this particular case, we wants the material to be transparent to the electron so that electrons get transmitted through the material and provide information about the materials.
Wehnelt electrode - an electrode in the electron gun assembly of some thermionic devices, used for focusing and control of the electron beam. A Wehnelt acts as a control grid and it also serves as a convergent electrostatic lens. An electron emitter is positioned directly above the Wehnelt aperture, and an anode is located below the Wehnelt. The anode is biased to a high positive voltage (typically +1 to +30 kV) relative to the emitter so as to accelerate electrons from the emitter towards the anode, thus creating an electron beam that passes through the Wehnelt aperture.
After coating tungsten tip with zirconium oxide operating temperature of tungsten reduces from 2700 K to 1800 K.
To get high field strength with low applied bias, field emitting tips are made sharp.
Changing converging point of the beam, some part of the beam is going to be cut and we will get small spot size i. e. low current and high resolution.
The second lens that we have is called objective lens. Based on changing the lens strength we can change the poit at which the system focuses.
Energy dispersive x-ray spectroscopy is techniques used for elemental analysis or chemical composition of the elements
